Does removing dead skin or trimming nails after performing ablution (wudu'), or the presence of white residue around the nails, or an oily layer on the nose, or forgetting the order of ablution and re-intending for it, invalidate the ablution or necessitate its repetition?

Removing skin or nails after performing ablution (wudu') does not invalidate the ablution and does not necessitate its repetition, unless the removed layer was an impediment preventing water from reaching the nail, in which case the ablution must be repeated.

As for white residue around the nails and fatty secretions, if they form a substance that prevents water from reaching the skin, they must be removed; otherwise, their presence does not cause harm.

The intention for ablution is not invalidated by forgetting it during the ablution; rather, its ruling remains in effect. If it is forgotten while washing some limbs and then remembered, there is no need to repeat the ablution; rather, one continues from where they left off. If one severs the intention of ablution, they must renew it and complete washing the remaining limbs of purification.